SOLUTION: 7x - 2y = 4 5y + 3x = 10 thank you

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Question 147013: 7x - 2y = 4
5y + 3x = 10
thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5y+%2B+3x+=+10+ Start with the second equation.


3x%2B5y=10 Rearrange the terms.



Start with the given system of equations:
system%287x-2y=4%2C3x%2B5y=10%29


5%287x-2y%29=5%284%29 Multiply the both sides of the first equation by 5.


35x-10y=20 Distribute and multiply.


2%283x%2B5y%29=2%2810%29 Multiply the both sides of the second equation by 2.


6x%2B10y=20 Distribute and multiply.


So we have the new system of equations:
system%2835x-10y=20%2C6x%2B10y=20%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2835x-10y%29%2B%286x%2B10y%29=%2820%29%2B%2820%29


%2835x%2B6x%29%2B%28-10y%2B10y%29=20%2B20 Group like terms.


41x%2B0y=40 Combine like terms. Notice how the y terms cancel out.


41x=40 Simplify.


x=%2840%29%2F%2841%29 Divide both sides by 41 to isolate x.


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35x-10y=20 Now go back to the first equation.


35%2840%2F41%29-10y=20 Plug in x=40%2F41.


1400%2F41-10y=20 Multiply.


41%281400%2Fcross%2841%29-10y%29=41%2820%29 Multiply both sides by the LCD 41 to clear any fractions.


1400-410y=820 Distribute and multiply.


-410y=820-1400 Subtract 1400 from both sides.


-410y=-580 Combine like terms on the right side.


y=%28-580%29%2F%28-410%29 Divide both sides by -410 to isolate y.


y=58%2F41 Reduce.


So our answer is x=40%2F41 and y=58%2F41.


Which form the ordered pair .


This means that the two equations are consistent and independent.